That A-Ha Moment

Larry Desjardin asks the readers about their moments of sudden insight.

Have you ever had an a-ha moment? Sure, you have. The Merriam-Webster dictionary defines it as "a moment of sudden realization, inspiration, insight, recognition, or comprehension." But I'm taking it one step further -- a-ha! with an exclamation point. This is a more dramatic realization. It's the moment when you discover a great truth, when something that was complicated or unpredictable suddenly becomes clear. As engineers, I'm sure we've had many.

One of my first a-ha!s came in grade school. I was a hobbyist, and I enjoyed creating things from the local Radio Shack, even though I didn't know why they worked. I had hoarded quite the collection of resistors, capacitors, tubes, and speakers. I could read the color bands on a resistor to get its value, and I had rudimentary soldering skills, but I didn't know how to design anything. One day, my older brother, who had been a Navy technician, explained Ohm's Law to me. A lightning bolt ignited in my head. You mean, there's a relationship between voltage, current, and resistance? That makes a lot of sense. And the world became a little bit more understandable. Building a circuit was a little less about pleasing the electron gods and a little more like engineering.

I've had several of these moments since then. Calculus was a key ingredient to many. Though I knew formulas from high school physics, calculus enabled me to derive the formulas. As a ham radio operator, I knew how to calculate the resonate frequency of an LC network.

But I didn't know why that was the resonant frequency. With calculus, I was able to derive it myself, and I discovered why it also explained the resonant frequency of a pendulum or a spring and mass. Calculus explained that the current through a capacitor was proportional to the first derivative of the voltage. Suddenly, first-order differential equations explained time-domain and frequency-domain phenomena. This was another a-ha! moment.

I've had many since then. Boolean logic explained digital circuits to me -- no longer a mystery. A more recent a-ha! moment came when I learned how WCDMA worked. In retrospect, all these things seem obvious, but I can recall the very day that each of these a-ha! moments came.

Science and engineering aren't the only subjects that have created these moments. An Economist article about international trade led the reader through a simplified two-party, two-industry model, where one party had a productivity advantage for both industries, and the other party had inferior productivity for both. Much to my surprise, simple arithmetic in the example showed that both parties produced and acquired more goods than either one could have done by itself if trading could occur between them. Until I had done the math, I had assumed trade was only advantageous if each had an absolute advantage in some industry. This was the principle of comparative advantage -- and another a-ha! moment for me. I remember the day I did the surprising arithmetic.

saeEE, did you know that you can embed videos in your comments> I went to the lind and got the embed code. But, I had to create a custom size because of the column width. This one is 360 wide x 270 high.

I just copied the code from YouTube, clicked on the HTML button below the entry field, cna pasted in the code.

My moment came almost 40 years ago, and it was much more than an "a-ha" moment. I was working on a hobby project with the CMOS 4000 series of logic circuits. I needed to divide two numbers in storage registers, but none of the books I had on logic circuits had any examples for me to work with. Young an inexperienced, I just kept on trying knowing that there must be a solution to my problem because others had done it in CPU's. For over two weeks I pondered the problem at least two hours each day without any resolution. One morning I woke up and immediately realized that knew how to make the circuit work. Clear as a bell. The best I can figure is that my brain, over the last few days, was working on the problem while I was sleeping and solved it before I woke up.

My most recent A-HA! moment was dicovering I could edit or delete my own EETimes comments (there's a link at the bottom of your own comments to do this)! Great for those moments just after you've posted something and realise it makes no sense at all......

A-ha! moments are great. I don't think there's anything gives you such a sense of satisfaction as realising you've just cracked something you thought you would never understand.

Many things I learned in school, I learned imperfectly, so a-ha moments have happened for me often. Now if only I could draw a free-body diagram correctly! And of course, if you went to school during the 80's, you might remember this a-ha moment :)